How do minimal tree generators work?

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SUMMARY

Minimal tree generators are rooted in Graph Theory and discrete mathematics, focusing on constructing minimal spanning trees. The process involves two sets: Remaining Nodes (A) and Visited Nodes (B). The algorithm initiates with the minimal edge, defined as the edge with the smallest weight, and iteratively transfers nodes from A to B based on the minimal connecting edge. Kruskal's algorithm, a specific implementation, begins with no edges and adds the smallest-weight edge that avoids cycle formation.

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  • Understanding of Graph Theory concepts
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  • Basic principles of discrete mathematics
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esmeco
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I was wondering,could someone explain me how do minimal tree generators work?
 
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Is this a Graph Theory or discrete math topic? Is it the minimal tree of the entire graph or connected to some node? mathworld.com

either way its about having 2 sets...the set of Remaining Nodes A and the set of nodes you have visited B. The idea is to move nodes in A to B. The algorithm will always start off with the minimal edge(one with the smallest weight). From there you iterate till no more nodes can be connected to B or A is empty. The criteria for moving a node from A to B is simply the minimal edge that connects A to B.
 
Kruskal's algorithm works differently, starting with no edges and continuing to add the smallest-weight edge that does not form a cycle.
 

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